Abstract:

Usually, anti-realistic conceptions of truth and falsity are based on the notions of proof and refutation (or disproof). In this tradition, the logic of anti-realistic truth and falsity is some kind of constructive logic: intuitionistic logic, bi-intuitionistic logic, or some constructive logic with strong negation. However, this inferentialist approach is not the only possible avenue to an anti-realistic conception of truth and falsity. Another perspective emerges from Nuel Belnap's idea of considering information sources that provide 'told values' for atomic propositions. A given atomic proposition may be just told to be true, just told to be false, neither told to be true nor told to be false, or both told to be true and told to be false. In this talk I will take Belnap's idea as a starting point for developing an anti-realistic conception of truth and falsity. I will draw on recent work by Sergei Odintsov and material presented in Y. Shramko and H. Wansing, Truth and Falsehood. An Inquiry into Generalized Logical Values, Springer-Verlag, 2011. In this approach the told values are lattice-ordered according to their degree of truth and their degree of falsity. The idea is that a proposition is logically true (false) iff for every assignment of told values to the atomic propositions, it receives as its value the top-element of the truth order (falsity order).